This project will continue the work on statistical methods used with censored survival data that was funded in the last grant period. The questions studied fall into three main areas: censored data regression methods; significance testing procedures for two or more samples of censored data; and a unified treatment of the martingale approach to the analysis of counting processes and censored data. In censored data regression, we will study: (a) diagnostics for proportional hazards regression methods based on generalized residuals for these models and on an improved kernel estimation method for hazard functions; (b) models for survival data with time dependent hazard ratios, especially models in which covariate effects diminish over time; (c) flexible data analytic proportional hazards models in which non-linear covariate effects are estimated with splines; and (d) methods for adjusting for covariate measurement errors with censored data. Significance testing procedures will include: (a) extensions of the work of O'Sullivan and Fleming (1986) on non-rank, asymptotically nonparametric methods for censored failure time data; (b) methods for evaluating the therapeutic index of new pharmaceutical agents being studied by Federal regulatory agencies; (c) extensions of paired data methods for censored data; and (d) methods for estimating treatment effects in trials using group sequential designs. Work on the now partially completed research monograph will be extended to include simplified proofs of asymptotic results for censored data testing and regression methods and a unified treatment of the proportional hazards regression model.